The supersonic flow past a wedge with large curved boundary

In this paper, we construct a piecewise smooth solution for a 2-D supersonic potential flow past a curved wedge, whose boundary is assumed to have large variation. In fact, we originally provide a background solution, which is constructed by assuming the coming flow has limit speed. Its shock coincides with the curved wedge and the flow behind the shock is defined only along the wedge. Then our problem can be treated as a perturbation of this background solution and the solution is obtained by showing specific estimates.